A fluoroscope, also known as a C-arm due to its “C” shape, is often used intra-operatively for visualizing underlying anatomy and surgical instruments. Though its applications in interventional disciplines are persuasive, its disadvantages are also apparent. A fluoroscopy image is a two-dimensional (2D) projection image, which lacks depth information. The image is distorted and has limited field of view. Its ability in providing three-dimensional (3D) quantitative information is limited and its application involves high radiation exposure to the interventional team. This has led to the development of methods for precise C-arm calibration1, 2, 3, 4, which are important for various fluoroscopy image based applications.
The goal of the calibration is to correct the geometric image distortion and to estimate the projection parameters of the x-ray apparatus (e.g. C-arm). For this purpose, a cage with fiducials arranged in multiple planes is normally required to be attached to the image intensifier, which has the disadvantage of interfering with the patient anatomy being imaged and requires tracking of the C-arm machine by an external tracker, which sometimes is judged to be too cumbersome.
There exist attempts to replace the external tracker with a mobile phantom. Yao et al.7 proposed to use a line fiducial based phantom mounted on a robot's tool holder to register the end effector of the surgical robot to a C-arm image. Inspired by this work, Jain and Fichtinger8 developed a new phantom that used ellipses and straight lines as fiducials in addition to points. Although encouraging results were presented with this new phantom8, it was recently reported by Otake et al.9 that automatic segmentation of this phantom from an intra-operatively acquired image was not always possible due to severe background clutter. They thus proposed to use a manually initialized, model-based iterative 2D-3D registration for an accurate detection of the phantom from the image.
Attempts to characterize the C-arm distortion with a statistical framework have previously been done by Chintalapani et al.5 ,6. Based on a statistical model of the geometrical image distortion, Chintalapani et al. discussed using fewer fiducials5 or even using the patient CT6 as a fiducial for distortion correction. The limitation of their work is that they only use images acquired from a fixed position by rotating the arm to build the statistical model of the distortion pattern such that the influence of the earth magnetic field on the image distortion was not estimated. It has been shown that such an influence contributes a lot to the image distortion and it is position dependent2, 7.